It's easy to armchair quarterback issues like these. From a macro perspective, killing anyone, especially a child, is a pretty horrible thing to fathom. The testosterone in some of us says "suck it up" and "I'd have no problem defending my family", and that's all good and well, but there are too many perspectives missing from your thought process if that's the only angle being considered. Likewise, steadfast advocates of absolute non-violence, while noble, paint a moral contrast of this issue with limited situational experience.
So, some perspective if you care for it.
I've seen this first hand from a sort of disconnected position - a 42" LCD television screen streaming an ISR feed, to be exact. You hear the aircraft in the sky, you have direct communication with the pilot, and you know the event is happening 2-3 clicks from your highschool-sized dirthole. But you're not Saving Private Ryan or any other visual point of reference you may have about full-scale war.
It's 2AM, you're observing the aircraft feed that just came on station in response to your reports of suspicious activity on a popular roadway. Someone appears to be digging and is in possession of container giving off a strong heat signature, an indicator of explosive materials. Your guys on the ground are about a click away, and from their night vision optics, all they see is a fuzzy cold spot moving around in ways that suggest IED emplacement.
Three days ago, you played poker with the guys in logistics. You only like 2 of them, specifically "Copley". You don't really know him too well, but he's got a great sense of humor and a pretty pleasant outlook on life, so you talk to him frequently when you see him. His convoy left for a resupply on the very same road you're surveilling right now. They hit an IED in a similar location, instantly rendering Copley a double amputee. You get woken up to the emergency because you need to facilitate the medivac, and for a grueling hour, you're telling officers to fuck off in an effort to save a stranger's life. In the lull moments, you wonder how things will be different for him, for his daughter and wife back home. It leaves a really uneasy feeling inside of your stomach and you've never felt more stressed to be competent at what you do than you do now.
As a side note, this is where critics will begin to chime in. People might say, "it was your decision to join the military, so when you get hurt, you'll get no sympathy here." And that's fair. But it also assumes that the oddly mixed population of the military (intelligent folks, products of the poor economy, legacy patriots, and farmboys) have some sort of evil agenda, as though they aren't just as victim to a warring state with a propaganda machine as the Pakistani farmer is to the Islamist extremist rule. Now, if you agree with that sentiment, but still say it's not an excuse for us to "blindly follow orders", then continue reading. I think this perspective will help you.
Believe it or not, the process to get the approval to employ an airstrike is a drawn-out marathon of red-tape and back-and-forth between echelons in order to prevent CIVCAS, or civilian casualties. None of you want that situation to happen. But this is clear that you have an IED emplacer, and Copley is still fresh in all of your minds. Now that you know this is a threat, you want to stop them as soon as possible and from future opportunities.
Approval to the aircraft is given, and the process to employ begins. Within 10 minutes, you watch in one instant as the IED emplacer begins moving the contents of the container into the hole suddenly turns into a cloud of white-hot and kicked-up dirt. The disconnect becomes very apparent, as you watch almost routinely as someone just lost their life from the confines of a small room on a television manufactured by Sony.
The guys on the ground move to the location for an assessment, and it comes back the it was a girl, probably in her teens, and she was in fact emplacing ball bearings and other explosive materials, told to do so by her poor farmer father who was given money by the real threat - he just wants to eat tomorrow, and the Taliban know exactly what they're doing when they hide behind civilians.
The sunken stomach feeling felt from Copley's situation sneaks back into you. You weigh the choices, and there's no easy conclusion to be made from this scenario. You conclude that the whole thing is complete shit, and it reaffirms just how awful circumstances are for the general population of Afghanistan.
I hope this narrative highlights the complexity of situations like these. Is there a cold, evil politician or military leader at the top of a chain somewhere commanding these kills with the press of a little red button in an unethical and morally corrupt fashion? Maybe, but I don't know.
For us bottom feeders, we didn't care about that shit. We wanted to survive the day, most of us thought the mission was bull shit, and many were well aware that the modern day military is a giant social experiment. We loved having these kids as friends in the bazaars, and were definitely not mindless drones. I know far too many people, officers alike, to tell superiors to fuck off in the face of bullshit orders.
This wasn't meant to answer the question, but instead to offer some new flavors of food for thought.